Solve for all values of x in simplest form. 41=|x+4| Answer: x=

Understand absolute value equation: Understand the absolute value equation. The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, |x + 4| can be either x + 4 or -(x + 4) if x + 4 is positive or negative, respectively. We need to consider both cases to find all values of x.Set up two equations: Set up two separate equations to solve. Since the absolute value of x + 4 is equal to 41, we have two possible equations: 1) x + 4 = 41 2) -(x + 4) = 41Solve first equation: Solve the first equation. Starting with x + 4 = 41, we subtract 4 from both sides to isolate x: x + 4 - 4 = 41 - 4 x = 37Solve second equation: Solve the second equation. Now, we solve -(x + 4) = 41. First, we distribute the negative sign: -x - 4 = 41 Next, we add 4 to both sides to isolate -x: -x - 4 + 4 = 41 + 4 -x = 45 Finally, we multiply both sides by -1 to solve for x: x = -45

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Solve for all values of
x in simplest form.

41=|x+4|
Answer:
x=

Solve for all values of $x$ in simplest form. $\newline$ $41=|x+4|$ $\newline$ Answer: $x=$

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Math Problems

Grade 6

Multiply numbers ending in zeros

Full solution

Q. Solve for all values of

x

in simplest form.

\newline

41=|x+4|

\newline

Answer:

x=

Understand absolute value equation: Understand the absolute value equation. $\newline$ The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, $|x + 4|$ can be either $x + 4$ or $-(x + 4)$ if $x + 4$ is positive or negative, respectively. We need to consider both cases to find all values of $x$ .
Set up two equations: Set up two separate equations to solve. $\newline$ Since the absolute value of $x + 4$ is equal to $41$ , we have two possible equations: $\newline$ $1$ ) $x + 4 = 41$ $\newline$ $2$ ) $-\left(x + 4\right) = 41$
Solve first equation: Solve the first equation. $\newline$ Starting with $x + 4 = 41$ , we subtract $4$ from both sides to isolate $x$ : $\newline$ $x + 4 - 4 = 41 - 4$ $\newline$ $x = 37$
Solve second equation: Solve the second equation. $\newline$ Now, we solve $- (x + 4) = 41$ . First, we distribute the negative sign: $\newline$ $-x - 4 = 41$ $\newline$ Next, we add $4$ to both sides to isolate $-x$ : $\newline$ $-x - 4 + 4 = 41 + 4$ $\newline$ $-x = 45$ $\newline$ Finally, we multiply both sides by $-1$ to solve for $x$ : $\newline$ $x = -45$